If a baseball is thrown 30 m/s backwards from a truck moving 50 m/s, how fast will the ball strike the glove of a ground-based catcher?
If the catcher is behind the truck when the ball is thrown, the ball will never get there. I will still have a forward velocity with respect to ground.
If the catcher faces away from the oncoming truck and the ball is thrown before the truck passes, he might have a chance of catching it at 20 m/s relative velocity
To find the speed at which the ball strikes the glove of the catcher, we need to consider the relative motion between the ball and the catcher.
Since the ball is thrown backward from the truck, we can consider its velocity as negative (-30 m/s). The truck is moving forward with a velocity of 50 m/s, but since we want to find the relative velocity of the ball with respect to the catcher, we subtract the truck's velocity from the ball's velocity:
Relative velocity of the ball = Ball's velocity - Truck's velocity
= (-30 m/s) - (50 m/s)
= -80 m/s
The negative sign indicates that the ball and the catcher are moving in opposite directions.
The catcher is stationary on the ground, so the velocity of the catcher is 0 m/s.
To find the speed at which the ball strikes the catcher's glove, we take the absolute value of the relative velocity since speed is a scalar quantity:
Speed at which the ball strikes the glove = |Relative velocity of the ball|
= |-80 m/s|
= 80 m/s
Therefore, the ball will strike the glove of the ground-based catcher with a speed of 80 m/s.